2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227256We explore the low-temperature behavior of the Abelian Higgs model in AdS_4, away from the probe limit in which back-reaction of matter fields on the metric can be neglected. Over a significant range of charges for the complex scalar, we observe a second order phase transition at finite temperature. The symmetry-breaking states are superconducting black holes. At least when the charge of the scalar is not too small, we observe at low temperatures the emergence of a domain wall structure characterized by a definite index of refraction. We also compute the conductivity as a function of frequency.17 pages, 3 figures. v2: corrected minor errorsHigh Energy Physics - Theorytext